is it normal for my new iPad air to overheat and randomly close out of apps not even a week after purchasing

Let’s define “overheating”. If an iPad overheats it shuts down so it can’t be used, and displays a message saying it must cool down before it can be turned on, and it will probably be unusable for an hour or so. If you are seeing this it is a hardware problem and you should contact Apple support: 

• Click on “Support” at the top of this page
• Go to Contact Official Apple Support

Note that both of the above have options to receive a callback or chat

If you are not seeing this your iPad has not overheated. However, if you fast charge your iPad may get very warm, pause charging at 80% and display a message saying that charging has paused, and will resume when the phone cools down. This is NOT overheating, and is normal when fast charging. It also won’t prevent you from using any app you have on your iPad.

Also, some apps that use a lot of energy or that use cellular data (if it's a cellular model) rather than Wi-Fi can cause the phone to run warmer.

It is not unusual for an iPad to become warm when being used - more so when using some types of iPad case. High screen brightness and/or CPU intensive Apps will also create more heat.

The key point is that whilst your iPad may become very warm in normal use, the iPad should not become uncomfortably hot to handle. If your iPad is becoming too hot to hold, you should take your iPad along to the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians can examine and test your iPad for faults:

Genius Bar Reservation and Apple Support Options - Apple